<![CDATA[Atheist Forums - Mathematics]]> https://atheistforums.org/ Sun, 28 Jun 2026 06:33:05 +0000 MyBB <![CDATA[One Hundred Prisoners]]> https://atheistforums.org/thread-66652.html Thu, 26 Mar 2026 02:14:47 +0000 https://atheistforums.org/thread-66652.html
The Problem:

There are 100 Prisoners being condemned to prison for all eternity.

Everybody in this scenario behaves purely logically and flawlessly, including not dying unless told to by the rules.

Prior to being incarcerated, the Prisoners are allowed to strategize. They will have no direct communication once their sentence begins.

Once their sentence begins, one prisoner will be selected purely at random* each day. That prisoner will be taken to a room with a light and a switch. The light may be turned on or off, but may not be manipulated in any other manner**.

Once they are certain*** that every prisoner has been in the room at least once, they may ask to be released. If they're right then they'll be freed, but if they're wrong they'll be executed.



OK, that's it. I think that I have both a brute force and an optimized solution. The brute force approach works, but it takes geological time. The optimized strategy might be viable within a human lifespan, maybe faster. I was wondering if there were quicker approaches and if anybody with a math/computing background knew how to calculate the time for the strategy to succeed.

Brute Force Strategy:


Optimized Strategy:

]]>
The Problem:

There are 100 Prisoners being condemned to prison for all eternity.

Everybody in this scenario behaves purely logically and flawlessly, including not dying unless told to by the rules.

Prior to being incarcerated, the Prisoners are allowed to strategize. They will have no direct communication once their sentence begins.

Once their sentence begins, one prisoner will be selected purely at random* each day. That prisoner will be taken to a room with a light and a switch. The light may be turned on or off, but may not be manipulated in any other manner**.

Once they are certain*** that every prisoner has been in the room at least once, they may ask to be released. If they're right then they'll be freed, but if they're wrong they'll be executed.



OK, that's it. I think that I have both a brute force and an optimized solution. The brute force approach works, but it takes geological time. The optimized strategy might be viable within a human lifespan, maybe faster. I was wondering if there were quicker approaches and if anybody with a math/computing background knew how to calculate the time for the strategy to succeed.

Brute Force Strategy:


Optimized Strategy:

]]> <![CDATA[RE: Solving a system of two trigonometric equations]]> https://atheistforums.org/thread-66427.html Tue, 20 May 2025 22:11:06 +0000 https://atheistforums.org/thread-66427.html
1)  atan(2/x) - atan(2/p) = -pi / 30

and  

2)    2/p / 2/x = x / p =12.6        

Also the  the solution to the problem was supposed to be x = 0.2 and p = 0.016    

In actuality the the solution isn't nice and neat and though there is an exact solution one needs to cut off to some acceptable decimal places I found x = 0.2286 and p = 0.01814

Its always difficult to describe a solution verbally but the problem isn't exactly so much a system of equations problem as it is a trigonometric problem, and going back to the basics.  First one must recognize that statement 1) is the difference between two angles so atan(2/x) is an angle we'll call A and atan(2/p) is angle B   So  1) becomes A - B = -pi/30  

Then  tan(A) = 2/x   and tan(B) = 2/p   thus if we draw two right triangles we have one with a height 2 and base x, and the other height 2 and base p   but here's the trick  p = x/a  so tan(B)= 2a/x.  Therefore we can draw two right triangles with the same base x and one with height 2 and the other with height 2 a.  

We can then superimpose the two right triangles one over the other because the bases are both x.    Now with  this configuration an isosceles triangle is formed within whose sides are all determined via right triangle trig.  Because we have three sides and three angles we can then apply the law of sins to the isosceles triangle.   From the Law of Sines we can determine x because the problem reduces to a 4th order quadratic equation.  We can reduce the 4th order variable   using a substitution s = x^2.  Then we solve for z using the quadratic formula and then solve for x once by taking the square root of z.  If you are able to open up the five sheets in the google drive link I shared, I have provided a step by step solution.   Its a pretty cool problem.   Now I haven't seen a problem quite  like this one before and I found it satisfying to solve.  

The step by step solution is uploaded on the  Google Drive and put the link to the drive below. There are five jpgs each numbered in order at the top right corner.  Hopefully anyone interested can access the five sheets.  

Pete Jeuck

Administrator Notice
Link removed per 30/30 rule.  This is your last freebie.  My suggestion is to read our rules.
]]>
1)  atan(2/x) - atan(2/p) = -pi / 30

and  

2)    2/p / 2/x = x / p =12.6        

Also the  the solution to the problem was supposed to be x = 0.2 and p = 0.016    

In actuality the the solution isn't nice and neat and though there is an exact solution one needs to cut off to some acceptable decimal places I found x = 0.2286 and p = 0.01814

Its always difficult to describe a solution verbally but the problem isn't exactly so much a system of equations problem as it is a trigonometric problem, and going back to the basics.  First one must recognize that statement 1) is the difference between two angles so atan(2/x) is an angle we'll call A and atan(2/p) is angle B   So  1) becomes A - B = -pi/30  

Then  tan(A) = 2/x   and tan(B) = 2/p   thus if we draw two right triangles we have one with a height 2 and base x, and the other height 2 and base p   but here's the trick  p = x/a  so tan(B)= 2a/x.  Therefore we can draw two right triangles with the same base x and one with height 2 and the other with height 2 a.  

We can then superimpose the two right triangles one over the other because the bases are both x.    Now with  this configuration an isosceles triangle is formed within whose sides are all determined via right triangle trig.  Because we have three sides and three angles we can then apply the law of sins to the isosceles triangle.   From the Law of Sines we can determine x because the problem reduces to a 4th order quadratic equation.  We can reduce the 4th order variable   using a substitution s = x^2.  Then we solve for z using the quadratic formula and then solve for x once by taking the square root of z.  If you are able to open up the five sheets in the google drive link I shared, I have provided a step by step solution.   Its a pretty cool problem.   Now I haven't seen a problem quite  like this one before and I found it satisfying to solve.  

The step by step solution is uploaded on the  Google Drive and put the link to the drive below. There are five jpgs each numbered in order at the top right corner.  Hopefully anyone interested can access the five sheets.  

Pete Jeuck

Administrator Notice
Link removed per 30/30 rule.  This is your last freebie.  My suggestion is to read our rules.
]]> <![CDATA[The Truth: The Mathematical Proof of God, The Holy Trinity]]> https://atheistforums.org/thread-66322.html Thu, 30 Jan 2025 20:36:48 +0000 https://atheistforums.org/thread-66322.html Administrator Notice
Deleted wall o' text (copy/paste) and multiple pics from our new and soon to be gone person. ]]> Administrator Notice
Deleted wall o' text (copy/paste) and multiple pics from our new and soon to be gone person. ]]> <![CDATA[Math game]]> https://atheistforums.org/thread-65489.html Thu, 28 Sep 2023 02:36:46 +0000 https://atheistforums.org/thread-65489.html ]]> ]]> <![CDATA[What does maths add up to?]]> https://atheistforums.org/thread-65353.html Fri, 25 Aug 2023 03:36:19 +0000 https://atheistforums.org/thread-65353.html <![CDATA[In nonsense]]> https://atheistforums.org/thread-65295.html Wed, 16 Aug 2023 02:19:58 +0000 https://atheistforums.org/thread-65295.html adds up like nothing else.
Nonsense is magic.]]> adds up like nothing else.
Nonsense is magic.]]> <![CDATA[Solving a system of two trigonometric equations]]> https://atheistforums.org/thread-65011.html Fri, 19 May 2023 18:12:39 +0000 https://atheistforums.org/thread-65011.html
omega_lb1 / omega_ln1 = 12.6
atan(2 / omega_lb1) - atan(2 / omega_ln1) = -6 deg

Allegedly, the solution is:

omega_lb1 = 0.2 rad/sec
omega_ln1 = 0.016 rad/sec

But how can that system of equations be solved?]]>
omega_lb1 / omega_ln1 = 12.6
atan(2 / omega_lb1) - atan(2 / omega_ln1) = -6 deg

Allegedly, the solution is:

omega_lb1 = 0.2 rad/sec
omega_ln1 = 0.016 rad/sec

But how can that system of equations be solved?]]> <![CDATA[Doing algebra with infinite series is very risky]]> https://atheistforums.org/thread-64885.html Wed, 08 Mar 2023 20:47:19 +0000 https://atheistforums.org/thread-64885.html
I'll reiterate this here:

x = 1 + 2 + 4 + 8 + 16 + ...
2x = 2 + 4 + 8 + 16 + 32 + ...
x = 1 + 2x
x - 2x = 1
-x = 1
x = -1

But x is supposed to be a divergent infinite series, so the sum can't amount to a finite number (such as -1)! What gives then?

I've been reading what other people online had to say about this, and many of them say the issue lies with one of the steps involving an "infinity minus infinity" which is indeterminate (in much the same way as 0/0 is indeterminate).

Namely, this step:
x - 2x = 1

I don't think the issue is with that. The answer is only indeterminate when we're dealing with infinity in an abstract sense. But here, we know what numbers are involved exactly in the infinite series, and so there is no issue with subtracting one well-defined infinite series from another.

The problem, in my opinion, is with the second step. We have 2x = 2 + 4 + 8 + 16 + 32 + ...

But 2x could also be 2x = x + x = 1 + 1 + 2 + 2 + 4 + 4 + 8 + 8 + 16 + 16 + ...

If we then move to the next step, it's not certain anymore that x = 1 + 2x.

The lesson to learn here? Doing algebra with infinite series is tricky as fuck. Don't take it for granted that doing so will lead you to a very intuitive answer.]]>
I'll reiterate this here:

x = 1 + 2 + 4 + 8 + 16 + ...
2x = 2 + 4 + 8 + 16 + 32 + ...
x = 1 + 2x
x - 2x = 1
-x = 1
x = -1

But x is supposed to be a divergent infinite series, so the sum can't amount to a finite number (such as -1)! What gives then?

I've been reading what other people online had to say about this, and many of them say the issue lies with one of the steps involving an "infinity minus infinity" which is indeterminate (in much the same way as 0/0 is indeterminate).

Namely, this step:
x - 2x = 1

I don't think the issue is with that. The answer is only indeterminate when we're dealing with infinity in an abstract sense. But here, we know what numbers are involved exactly in the infinite series, and so there is no issue with subtracting one well-defined infinite series from another.

The problem, in my opinion, is with the second step. We have 2x = 2 + 4 + 8 + 16 + 32 + ...

But 2x could also be 2x = x + x = 1 + 1 + 2 + 2 + 4 + 4 + 8 + 8 + 16 + 16 + ...

If we then move to the next step, it's not certain anymore that x = 1 + 2x.

The lesson to learn here? Doing algebra with infinite series is tricky as fuck. Don't take it for granted that doing so will lead you to a very intuitive answer.]]> <![CDATA[Why is 0⁰ = 1?]]> https://atheistforums.org/thread-64646.html Thu, 24 Nov 2022 02:14:40 +0000 https://atheistforums.org/thread-64646.html

[Image: fh8uh7mauaenux3.png]]]>

[Image: fh8uh7mauaenux3.png]]]> <![CDATA[What are your overall opinions on people who are idiots in math?]]> https://atheistforums.org/thread-64558.html Sun, 16 Oct 2022 02:08:11 +0000 https://atheistforums.org/thread-64558.html
I was told by a few educated people that certain individuals who tend to be great at either math or languages are usually abysmal on either while being great on the other. I guess I'm one of those people.

So... What do you think? Did I inherit bad math-brain chromosomes? Or am I just lazy when it comes to studying math? To be perfectly clear, I actually have a very sharp memory.]]>
I was told by a few educated people that certain individuals who tend to be great at either math or languages are usually abysmal on either while being great on the other. I guess I'm one of those people.

So... What do you think? Did I inherit bad math-brain chromosomes? Or am I just lazy when it comes to studying math? To be perfectly clear, I actually have a very sharp memory.]]> <![CDATA[I hate math]]> https://atheistforums.org/thread-64477.html Tue, 13 Sep 2022 12:40:26 +0000 https://atheistforums.org/thread-64477.html On youtube its called "Do you see"]]> On youtube its called "Do you see"]]> <![CDATA[A mathematical problem I can't seem to get Mathematica to auto solve.]]> https://atheistforums.org/thread-64165.html Sat, 21 May 2022 02:01:42 +0000 https://atheistforums.org/thread-64165.html Lets say for the function f1(n) that n=b+1/Powerroot(f1(n),b). So i'm trying to find the root dimension required for the sum to equal n quick.
The only reason I was studying this was because I wanted to see if there was any relationship with prime number distribution.]]> Lets say for the function f1(n) that n=b+1/Powerroot(f1(n),b). So i'm trying to find the root dimension required for the sum to equal n quick.
The only reason I was studying this was because I wanted to see if there was any relationship with prime number distribution.]]> <![CDATA[Bayesian Statistics]]> https://atheistforums.org/thread-64084.html Mon, 25 Apr 2022 21:24:34 +0000 https://atheistforums.org/thread-64084.html
I think part of my struggle comes from the hype around it being overly ambitious and taking it's inferences out of context (I think). You'll hear people say it's a way to update your beliefs, but since regular statistics isn't about beliefs it already feels like a separate thing all together.

Point is I'm trying to understand Bayesian statistics. So I'm curious what everyone's experience with it has been. What textbooks or resources you recommend. And any theoretical issues or debates you guys have with it.]]>
I think part of my struggle comes from the hype around it being overly ambitious and taking it's inferences out of context (I think). You'll hear people say it's a way to update your beliefs, but since regular statistics isn't about beliefs it already feels like a separate thing all together.

Point is I'm trying to understand Bayesian statistics. So I'm curious what everyone's experience with it has been. What textbooks or resources you recommend. And any theoretical issues or debates you guys have with it.]]> <![CDATA[Post your favorite proof]]> https://atheistforums.org/thread-64049.html Mon, 18 Apr 2022 17:23:04 +0000 https://atheistforums.org/thread-64049.html
For me, the following one takes the cake, it's hands down the most elegant "wow" proof I encountered, back when I was an undergraduate student:

         [Image: image.png]

[Image: image.png]

The proof is non-constructive. In other words, we don't really know what the two irrational numbers are (not without using the heavy machinery of modern math, at least) , and yet we know that the assertion is true!

And you? what's your favorite proof?]]>
For me, the following one takes the cake, it's hands down the most elegant "wow" proof I encountered, back when I was an undergraduate student:

         [Image: image.png]

[Image: image.png]

The proof is non-constructive. In other words, we don't really know what the two irrational numbers are (not without using the heavy machinery of modern math, at least) , and yet we know that the assertion is true!

And you? what's your favorite proof?]]> <![CDATA[Question: Proving the volume of a pyramid]]> https://atheistforums.org/thread-63893.html Thu, 03 Mar 2022 18:14:28 +0000 https://atheistforums.org/thread-63893.html <![CDATA[Is there an infinite range of perfect circles.]]> https://atheistforums.org/thread-63852.html Mon, 21 Feb 2022 23:29:49 +0000 https://atheistforums.org/thread-63852.html Also if you want understand how a glome or 4d N-Sphere works better what happens when starting from a line evolving dimensionally from a line to a box to a cube to a tesseract ect an inscribed N-Sphere and a line from the centre to the furthest corner type of the N-cube as it grows in dimension.
yes what does happen to that line that intersects the evolving inscribed N-sphere and the furthest corner of the evolving N-cube as the dimension shifts from 3d to 4d and how does a graphing of this curvature work regarding an evolving N-sphere intersection plot as it approaches infinity if you want to know more about curves discreetly represented on an infinite plane as to their approach that is.]]> Also if you want understand how a glome or 4d N-Sphere works better what happens when starting from a line evolving dimensionally from a line to a box to a cube to a tesseract ect an inscribed N-Sphere and a line from the centre to the furthest corner type of the N-cube as it grows in dimension.
yes what does happen to that line that intersects the evolving inscribed N-sphere and the furthest corner of the evolving N-cube as the dimension shifts from 3d to 4d and how does a graphing of this curvature work regarding an evolving N-sphere intersection plot as it approaches infinity if you want to know more about curves discreetly represented on an infinite plane as to their approach that is.]]> <![CDATA[How to solve this equation?]]> https://atheistforums.org/thread-63822.html Sun, 13 Feb 2022 15:07:15 +0000 https://atheistforums.org/thread-63822.html So, in my Introduction to Robotics class, we are supposed to solve, as a part of solving an example, this equation (page 12):
1/s+1/(s+2)+1/(s+6-2i)+1/(s+6+2i)=1/(s+1)
Now, the very next step we are given goes like this:
3s^4+32s^3+106s^2+128s+80=0
I do not understand how they got from the first equation to the second one. Can somebody here explain me that?]]> So, in my Introduction to Robotics class, we are supposed to solve, as a part of solving an example, this equation (page 12):
1/s+1/(s+2)+1/(s+6-2i)+1/(s+6+2i)=1/(s+1)
Now, the very next step we are given goes like this:
3s^4+32s^3+106s^2+128s+80=0
I do not understand how they got from the first equation to the second one. Can somebody here explain me that?]]> <![CDATA[What's the probability that 3 out of 23 people will share the same birthday?]]> https://atheistforums.org/thread-63756.html Fri, 21 Jan 2022 06:06:18 +0000 https://atheistforums.org/thread-63756.html I have written in this article about something distantly related to that, estimated numerically using Monte Carlo method that it is around 1.26%, and that the probability that 4 out of 23 people will share the same birthday is around 0.018%. However, I am interested whether there is a general formula for that.]]> I have written in this article about something distantly related to that, estimated numerically using Monte Carlo method that it is around 1.26%, and that the probability that 4 out of 23 people will share the same birthday is around 0.018%. However, I am interested whether there is a general formula for that.]]> <![CDATA[Is zero a natural number?]]> https://atheistforums.org/thread-63749.html Tue, 18 Jan 2022 10:35:04 +0000 https://atheistforums.org/thread-63749.html
In any case, I am going to buck the overwhelming trend among mathematicians as of late and say that zero is not a natural number and also say that the question of zero's "naturalness" is principally a question of anthropology and not of mathematics.  Some years ago I read a book, Zero: The Biography of a Dangerous Idea, and when the concept of zero was developed in India (and elsewhere) in the 7th century (or, thereabouts) and made its way to Europe, it was not greeted warmly; people were suspicious.  Here's an example of a modern-day ("money making") scholastic denying the existence of the number zero:






The segment in question is only 2 minutes long (if you can stand such), but, clearly, Dr. Craig, who was a communications major at Wheaton College, is having difficultly understanding the fact that numbers can be used as nominal values, but, that's another post.

In any case, the number zero is, in my opinion, not "natural", in the same sense that infinitesimals, limits, convergent/divergent series and non-Euclidean geometries are not natural.  What is certain is that the professional mathematicians, both pure and applied, are going to disagree!

P.S.  The YouTube link didn't paste correctly; you have to scroll to the 1:17:50 mark if you want to hear Dr. Craig's buffoonery.

P.P.S.  To Dr. Craig, "infinity" is not a number.]]>
In any case, I am going to buck the overwhelming trend among mathematicians as of late and say that zero is not a natural number and also say that the question of zero's "naturalness" is principally a question of anthropology and not of mathematics.  Some years ago I read a book, Zero: The Biography of a Dangerous Idea, and when the concept of zero was developed in India (and elsewhere) in the 7th century (or, thereabouts) and made its way to Europe, it was not greeted warmly; people were suspicious.  Here's an example of a modern-day ("money making") scholastic denying the existence of the number zero:






The segment in question is only 2 minutes long (if you can stand such), but, clearly, Dr. Craig, who was a communications major at Wheaton College, is having difficultly understanding the fact that numbers can be used as nominal values, but, that's another post.

In any case, the number zero is, in my opinion, not "natural", in the same sense that infinitesimals, limits, convergent/divergent series and non-Euclidean geometries are not natural.  What is certain is that the professional mathematicians, both pure and applied, are going to disagree!

P.S.  The YouTube link didn't paste correctly; you have to scroll to the 1:17:50 mark if you want to hear Dr. Craig's buffoonery.

P.P.S.  To Dr. Craig, "infinity" is not a number.]]> <![CDATA[Which error is this?]]> https://atheistforums.org/thread-63716.html Sun, 02 Jan 2022 03:37:02 +0000 https://atheistforums.org/thread-63716.html
Which formal structural error is this? Is it still considered Affirming the Consequent if they’re using negations of p and q in the second premise?

[Image: 945-A4-E0-F-80-E0-428-F-8977-D3-AF4446-D960.jpg]]]>
Which formal structural error is this? Is it still considered Affirming the Consequent if they’re using negations of p and q in the second premise?

[Image: 945-A4-E0-F-80-E0-428-F-8977-D3-AF4446-D960.jpg]]]>